Patrick Connolly

geophysics for integration

Patrick Connolly Associates Ltd.

Unmeasurable aspects of seismic data and implications for QI.

Defeated World Chess Champion Garry Kasparov in 1997

‘Advanced Chess’; humans + machines

2005 Tournament:• ‘Dream-teams’: Grandmasters + Computer scientists

• Won by Steven Cramton and Zackary Stephen; amateur players using laptops

• ‘We had really good methodology for when to use the computer and when to use our human judgement’

• ‘A clever process beat superior knowledge and superior technology’ - Garry Kasparov

Deep BlueMoravec's paradox

Computers and humans have complementary skills

Seismic Data Processing & Interpretation• Machines; applying decon, NMO and

migration operators• Humans; picking velocities, selecting optimal

parameters, interpretation

World leaders in optimising human + machine combination?

Seismic

Perhaps we are!

QI?

Because some aspects of seismic can’t be measured

Why can’t computers do everything?

field data

prospect

fully processed

inverted

Signal-to-noise

after noise reduction

signal

signal + noise

+ =

signal noise signal + noise5:1

Incoherent noise

Coloured Inversion

reflectivity band-limited impedance(colour inversion)

Signal changes but noise

doesn’t (?)

Fluid and lithology identification using high-resolution 3D seismic dataP. Connolly, S. Wilkins, T. Allen, G. Schurter & N. Rose-Innes,

Proceedings of the 6th Petroleum Geology Conference, 2005

Input reflectivity data

3-4-43-63Hz

8-9-43-63Hz

Trial & error

Output CI

• Flat gathers• Offset scaling• Offset spectral balancing• Offset to angle relationship• Truncation bias• Anisotropy• Moveout correction artefacts:

‒ NMO stretch‒ Offset tuning

• Random noise• Coherent noise:

‒ Multiples‒ Mode conversions‒ Residual noise

Gradient measurement errors

𝑠𝑠𝑠𝑠𝑠𝑠2𝜃𝜃 =𝑥𝑥2𝑉𝑉𝑖𝑖2

𝑉𝑉𝑟𝑟2 𝑉𝑉𝑟𝑟2𝑡𝑡02 + 𝑥𝑥2

where 𝑥𝑥 = offset𝑉𝑉𝑖𝑖 = interval velocity𝑉𝑉𝑟𝑟 = RMS velocity𝑡𝑡0 = zero offset TWT

West-of-Shetland Tertiary sonic

Blocked (22ms): ~seismic resolution

Smoothed (100ms): ~velocity resolution

Difference: % velocity error

• 5% errors unavoidable, 10% errors likely• Much larger errors quite possible

Angle estimation errors𝑅𝑅 𝜃𝜃 ≈ 𝐴𝐴 + 𝐵𝐵 sin2 𝜃𝜃

Offset scaling errors

Seismic Amplitude. An Interpreter’s Handbook, 2014, R. Simm and M. Bacon,

~10% difference

sin2θ

ampl

itude

30⁰

scaling uncertainty

𝐵𝐵𝑚𝑚 = 𝑆𝑆𝐵𝐵 + 4 𝑆𝑆 − 1 𝐴𝐴

𝐵𝐵 = true gradient𝑆𝑆 = scaling factor (1 = correct scaling)𝐵𝐵𝑚𝑚 = measured gradient

• 10% errors unavoidable• Much larger errors quite likely

Isotropic top brine sand ∆δ = -0.07 and ∆ε = -0.07

Offshore Angola well• layer 1 average shale values • layer 2 average brine-sand values.

Vp Vs rholayer 1 2743 1273 2.38layer 2 3113 1579 2.34

𝐴𝐴 =12

∆𝑉𝑉𝑃𝑃𝑉𝑉𝑃𝑃

+∆𝜌𝜌𝜌𝜌

𝐵𝐵 =∆𝑉𝑉𝑃𝑃2𝑉𝑉𝑃𝑃

− 2𝑘𝑘∆𝜇𝜇𝜇𝜇

+∆𝛿𝛿2

𝐶𝐶 =∆𝑉𝑉𝑃𝑃2𝑉𝑉𝑃𝑃

+∆𝜀𝜀2

𝑅𝑅 𝜃𝜃 ≈ 𝐴𝐴 + 𝐵𝐵 sin2 𝜃𝜃 + 𝐶𝐶 sin2 𝜃𝜃 tan2 𝜃𝜃

𝑉𝑉𝑃𝑃 90° = 𝑉𝑉𝑃𝑃 0° [1 + 𝜀𝜀]

𝑉𝑉𝑁𝑁𝑁𝑁𝑁𝑁 = 𝑉𝑉𝑃𝑃 0° [1 + 𝛿𝛿]

Anisotropy – the Rüger equation

*Weak anisotropy, 1986, Leon Thomsen, Geophysics

Typical sand/shale contrast for 𝛿𝛿 and 𝜀𝜀 = 0.07*

Isotropic top brine sand ∆δ = -0.07 and ∆ε = -0.07

Offshore Angola well• layer 1 average shale values • layer 2 average brine-sand values.

Vp Vs rholayer 1 2743 1273 2.38layer 2 3113 1579 2.34

Anisotropy – the Rüger equation

*Weak anisotropy, 1986, Leon Thomsen, Geophysics

Typical sand/shale contrast for 𝛿𝛿 and 𝜀𝜀 = 0.07*

Amplitude map – far offsets

contact

brine sands

𝑅𝑅𝑃𝑃 𝐴𝐴 𝐵𝐵 𝐶𝐶

λρ 3 1 0

Κρ 2.5 0.5 0

µρ 0.5 -0.5 0

SI 0.5 -0.5 0

Ερ 1.17 -0.83 0

⁄𝑉𝑉𝑃𝑃 𝑉𝑉𝑆𝑆 0.5 0.5 0

Κ 1.5 0.5 1

µ 0 -1 1

𝑘𝑘 = 0.25

Theory: elastic property reflectivity

𝑃𝑃 = elastic property (or product)

𝑅𝑅𝑃𝑃 = Δ𝑃𝑃2𝑃𝑃

= elastic property reflectivity

𝑅𝑅𝑃𝑃 = 𝑐𝑐1𝐴𝐴 + 𝑐𝑐2𝐵𝐵 + 𝑐𝑐3𝐶𝐶where

𝐴𝐴 = intercept𝐵𝐵 = gradient𝐶𝐶 = curvature

𝑅𝑅𝑃𝑃 𝐴𝐴 𝐵𝐵 𝐶𝐶 𝜒𝜒

λρ 3 1 0 18.4⁰

Κρ 2.5 0.5 0 11.3⁰

µρ 0.5 -0.5 0 -45⁰

SI 0.5 -0.5 0 -45⁰

Ερ 1.17 -0.83 0 -35.5⁰

⁄𝑉𝑉𝑃𝑃 𝑉𝑉𝑆𝑆 0.5 0.5 0 45⁰

Κ 1.5 0.5 1 ~12.3⁰

µ 0 -1 1 ~51.3⁰

𝑘𝑘 = 0.25

𝑘𝑘 = 0.25 & Gardner (C = 0.8A)

Theory: elastic property reflectivity

𝑃𝑃 = elastic property (or product)

𝑅𝑅𝑃𝑃 = Δ𝑃𝑃2𝑃𝑃

= elastic property reflectivity

𝑅𝑅𝑃𝑃 = 𝑐𝑐1𝐴𝐴 + 𝑐𝑐2𝐵𝐵 + 𝑐𝑐3𝐶𝐶where

𝐴𝐴 = intercept𝐵𝐵 = gradient𝐶𝐶 = curvature

𝑅𝑅𝑠𝑠 𝜒𝜒 = 𝐴𝐴𝑐𝑐𝐴𝐴𝑠𝑠 𝜒𝜒 + 𝐵𝐵𝑠𝑠𝑠𝑠𝑠𝑠(𝜒𝜒)

𝑅𝑅𝑃𝑃 𝐴𝐴 𝐵𝐵 𝐶𝐶 𝜒𝜒

λρ 3 1 0 18.4⁰

Κρ 2.5 0.5 0 11.3⁰

µρ 0.5 -0.5 0 -45⁰

SI 0.5 -0.5 0 -45⁰

Ερ 1.17 -0.83 0 -35.5⁰

⁄𝑉𝑉𝑃𝑃 𝑉𝑉𝑆𝑆 0.5 0.5 0 45⁰

Κ 1.5 0.5 1 ~12.3⁰

µ 0 -1 1 ~51.3⁰

𝑘𝑘 = 0.25

𝑘𝑘 = 0.25 & Gardner (C = 0.8A)

Theory: elastic property reflectivity

Chi error curvesangle error = 10%, variable scaling error

scaling error

Gradient measurements are in error;actual χ not equal to apparent χ

Theory: elastic property reflectivity

Chi error curvesangle error = 10%, variable scaling error

scaling error

Gradient measurements are in error;actual χ not equal to apparent χ

“No battle plan survives contact with the enemy”

- Field Marshall Helmuth von Moltke

“No theory survives contact with the data”

Chi scan

(simulated scan)

stack35⁰

The maximum signal-to-noise is shifted towards the stack chi value

But we can’t calculate the shift!

25⁰

Random noise

Noise

Reservoir Geological Model

Elastic Properties Ideal Seismic Real Seismic

Inversion to reservoir properties

inversion to reservoir properties

rock physics models

geological models

Reservoir Geological Model

Elastic Properties Ideal Seismic Real Seismic

Probabilistic inversion

prior likelihood

posterior

Bayes

But, we can’t measure uncertainties!

channel axis

mean: 0.7stdv: 0.08

channel margin

mean: 0.3stdv: 0.1

lithofacies proportions

Clean sand

Shaley sand

Shale

Cemented sand

Nor

mal

ised

prob

abili

ty &

coun

t

Proportion (%) Proportion (%)

Geological model

• Uncertainty measurements depend on the model.

• If the model is wrong the uncertainties will be too large, or too small.

Shale VP

dept

h be

low

dat

umWhat model would you fit to this?

Rock physics uncertainties

Uncertainty quantification is always subjective

Seismic uncertainty

+ =

signal noise signal + noise5:1

Incoherent noise

λρ (χ = 18⁰) µρ (χ = -45⁰)

gradient measurement error• 10% offset scaling error• 10% angle estimation error• 0.07 anisotropy (δ) contrastCoherent noise:

Seismic uncertainty

λρ (χ = 18⁰) µρ (χ = -45⁰)

gradient measurement error• 10% offset scaling error• 10% angle estimation error• 0.07 anisotropy (δ) contrastCoherent noise:Chi error curves

angle error = 10%, variable scaling error

scaling error

Actual χ not equal to apparent χ because of gradient measurement errors

Seismic uncertaintyChi error curves

angle error = 10%, variable scaling error

scaling error

Actual χ not equal to apparent χ because of gradient measurement errors

Characterise seismic uncertainty as uncertainty in

chi angle?

Will depend on chi value and subjective assessment of;• Scaling uncertainty• Angle uncertainty (velocity

uncertainty)• Anisotropy uncertainty• …

Well calibration?

487845934059

545046764676

597141403941

487845934059

545046764676

597141403941

25m25m

~±20%

Well-seismic positional uncertainty can result in

significant calibration uncertainty

P5 P25 P50 P75 P95

Mean net sand fraction

lithofacies(most likely)

Percentiles: Blueback ODiSI

Ranges depend on subjective uncertainty values

QI Workflows

Flattened gathers

intercept

gradient

Relative AI

Relative GI

Relative elastic

property A

Relative elastic

property B

1D facies probabilities

Probabilistic reservoir

properties

Coordinate rotations

1D probabilistic

inversion

Coloured inversion

Rock physics,

geological priors, …

Angle stacks

Simultaneous inversion

λρ fluid volume

µρ lithology volume

• No bandwidth optimisation• No gradient error mitigation• No uncertainty quantification

Summary

• QI workflows cannot be automated any more than processing workflows (yet).

• Focus on the largest unknowns and test options.

• Spread your workflows; use your judgement.

• Aim to develop ‘… good methodology for when to use the computer and when to use … human judgement’

“No theory survives contact with the data”

Acknowledgements

• Thanks to Cegal for Blueback ODiSI results.

• Thanks to Force for inviting me.

• Questions?

geophysics for integration